Question

find the surface area of the prism using the net. what is the area of the front and back rectangles? front and back rectangles:? cm² side rectangles: cm² top and bottom rectangles: cm² surface area: cm²

Explanation:

Step1: Calculate area of front and back rectangles

The front and back rectangles have dimensions 6 cm (height) and 4 cm (width). The area of a rectangle is $A = lw$. For the front - back rectangles, $l = 6$ cm and $w = 4$ cm. So the area of one such rectangle is $6\times4=24$ $cm^{2}$, and the combined area of front and back is $2\times24 = 48$ $cm^{2}$.

Step2: Calculate area of side rectangles

The side rectangles have dimensions 6 cm (height) and 1 cm (width). The area of a rectangle is $A=lw$. For side rectangles, $l = 6$ cm and $w = 1$ cm. So the area of one side rectangle is $6\times1=6$ $cm^{2}$, and the combined area of two side rectangles is $2\times6=12$ $cm^{2}$.

Step3: Calculate area of top and bottom rectangles

The top and bottom rectangles have dimensions 4 cm (length) and 1 cm (width). The area of a rectangle is $A = lw$. For top - bottom rectangles, $l = 4$ cm and $w = 1$ cm. So the area of one top - bottom rectangle is $4\times1 = 4$ $cm^{2}$, and the combined area of top and bottom is $2\times4=8$ $cm^{2}$.

Step4: Calculate surface area

The surface area of the prism is the sum of the areas of all rectangles. So, $SA=48 + 12+8=68$ $cm^{2}$.

Answer:

Front and back rectangles: $48$ $cm^{2}$
Side rectangles: $12$ $cm^{2}$
Top and bottom rectangles: $8$ $cm^{2}$
Surface Area: $68$ $cm^{2}$